Problem 63 - Chemistry and Chemical Reactivity

Question

To estimate the enthalpy change for the reaction $$\mathrm{O}_{2}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ what bond dissociation enthalpies do you need? Outline the calculation, being careful to show correct algebraic signs.

Step-by-Step Solution

Answer

-482 kJ/mol

Step 1: Identify Bonds in Reactants and Products

The reaction involves breaking the bonds in oxygen gas \( \mathrm{O}_{2}(\mathrm{g}) \) and hydrogen gas \( \mathrm{H}_{2}(\mathrm{g}) \) and forming bonds in water vapor \( \mathrm{H}_{2}\mathrm{O}(\mathrm{g}) \). We need to consider the \( \mathrm{O}=\mathrm{O} \) double bond, two \( \mathrm{H}-\mathrm{H} \) single bonds in the reactants and four \( \mathrm{O}-\mathrm{H} \) single bonds in the products.

Step 2: Write the Bond Dissociation Enthalpies

The bond dissociation enthalpies for each bond are as follows: 1. \( \mathrm{O}=\mathrm{O} \) double bond: 498 kJ/mol 2. \( \mathrm{H}-\mathrm{H} \) single bond: 436 kJ/mol 3. \( \mathrm{O}-\mathrm{H} \) single bond: 463 kJ/mol

Step 3: Calculate Total Enthalpy for Breaking Bonds

Calculate the total energy required to break the bonds in the reactants. This includes one \( \mathrm{O}=\mathrm{O} \) and two \( \mathrm{H}-\mathrm{H} \) bonds: \(\Delta H_{\text{break}} = 1 \times 498 + 2 \times 436 = 498 + 872 = 1370 \text{ kJ/mol}\)

Step 4: Calculate Total Enthalpy for Forming Bonds

Calculate the total energy released in forming the products' bonds. You form four \( \mathrm{O}-\mathrm{H} \) bonds: \(\Delta H_{\text{form}} = 4 \times 463 = 1852 \text{ kJ/mol}\)

Step 5: Determine the Enthalpy Change of Reaction

The enthalpy change of the reaction is calculated by subtracting the energy released from the energy required:\(\Delta H_{\text{reaction}} = \Delta H_{\text{break}} - \Delta H_{\text{form}} = 1370 - 1852 = -482 \text{ kJ/mol}\) This indicates that the reaction is exothermic.

Key Concepts

Bond Dissociation Enthalpy

Bond dissociation enthalpy refers to the amount of energy needed to break a particular type of chemical bond in one mole of gaseous molecules. It is a crucial concept in understanding how energy is exchanged during chemical reactions. For example, to estimate the enthalpy change in the reaction forming water vapor from oxygen and hydrogen gases, we must first consider the bonds involved.When breaking bonds, we calculate the energy needed to dissociate these bonds. In our reaction, we need to account for:

• the double bond in oxygen (\( \mathrm{O} = \mathrm{O} \)), and
• the single bonds in hydrogen (\( \mathrm{H} - \mathrm{H} \)).

For these bonds, specific bond dissociation enthalpies are given:

• \( \mathrm{O} = \mathrm{O} \): 498 kJ/mol, and
• \( \mathrm{H} - \mathrm{H} \): 436 kJ/mol.

These values illustrate the significant amount of energy needed to break these strong chemical bonds, a fundamental step in analyzing reactions.

Exothermic Reaction

Exothermic reactions release energy into their surroundings, typically in the form of heat. This process occurs when the energy released in forming new bonds is greater than the energy required to break the initial bonds. In the provided reaction, forming water vapor from oxygen and hydrogen gases demonstrates an exothermic process. Here, the energy required to break the bonds is less than the energy released from forming new water bonds. The calculated enthalpy change, \( \Delta H_{\text{reaction}} = -482 \text{ kJ/mol} \), indicates an exothermic reaction since it is negative.Exothermic reactions are common in everyday life, such as burning fuels or cellular respiration, and understanding them helps us appreciate how energy moves and transforms in nature.

Chemical Bonds

Chemical bonds are connections between atoms that enable the formation of molecules. Various types of chemical bonds include ionic, covalent, and metallic. In the context of our reaction, covalent bonds play a central role. Initially, there are significant bonds to consider:

• Double bonds in oxygen (\( \mathrm{O} = \mathrm{O} \)) are strong, requiring more energy to break, and
• Single bonds in hydrogen (\( \mathrm{H} - \mathrm{H} \)).

When water forms, oxygen and hydrogen create new single bonds (\( \mathrm{O} - \mathrm{H} \)) using shared electron pairs. Understanding these bonds helps us elucidate the energy changes in molecular transformations, emphasizing why certain reactions proceed as they do.

Water Formation

Water formation through chemical reactions is essential in both natural processes and industrial applications. The simple combination of hydrogen and oxygen to form water (\(2 \mathrm{H}_{2} \mathrm{O} \)) exemplifies this reaction with high relevance to energy transformations.In this reaction, two hydrogen molecules react with one oxygen molecule, leading to the creation of water vapor. This process involves breaking the original bonds:

• One oxygen double bond and
• Two hydrogen single bonds.

These breakages are energy-intensive and subsequently produce new bonds:

• Four newly formed single bonds between oxygen and hydrogen atoms.

The release of significant energy during these bond formations makes it an exothermic reaction. Understanding water formation gives insight into energy management in reactions, showcasing the practical applications of chemistry in power generation and use.